Primal and Dual Bregman Methods with Application to Optical Nanoscopy

Brüne, Christoph; Sawatzky, Alex; Burger, Martin

doi:10.1007/s11263-010-0339-5

Cited by 71 publications

(81 citation statements)

References 58 publications

(64 reference statements)

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“…These are the cardiomyocytes believed by Krehl [18] to provide the driving force for ventricular emptying. Perhaps more importantly, the quantitative, as opposed to qualitative, observations we were able to make using an automated system that avoids the need for subjective interpretation [16] confirm that a significant proportion of cardiomyocytes are aligned in a transmural fashion across the ventricular walls [11]. These measurements provided no support for the notion that all cardiomyocytes are aligned in a virtually tangential fashion.…”

Section: Histological Findingsmentioning

confidence: 84%

“…Fig. 3 The upper three rows of the figures show the distribution of helical angles (left hand panels) and transversely intruding angles (middle panels) as assessed using the computed tomographic images from the basal, middle, and apical thirds of the ventricular cone as measured using the computerderived system [16]. The right-hand panels show the location of the site of measurement relative to the long axis of the posterior ventricular wall (right panel).…”

Section: Computed Tomographymentioning

confidence: 99%

“…The points of measurement, therefore, refer to the relative thicknesses in the selected mural segments. Using an automatic, investigator-independent, computer-assisted technique depending on customized software based on algorithms described recently by Brune et al [16], we measured the angulations of the chains of cardiomyocytes in one single heart, assessing the changes in terms of both the helical and transmural directions. In the 2 hearts prepared for histological validation, we rinsed the coronary arteries with saline, inflated them for several minutes with compressed air, and perfused them with 4 % formaldehyde for 2 days, using a pressure of perfusion comparable to distension at 300 kilopascals.…”

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confidence: 99%

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Pneumatic Distension of Ventricular Mural Architecture Validated Histologically

Burg

Lunkenheimer

Niederer

et al. 2016

Fortschr Röntgenstr

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▼Purpose: There are ongoing arguments as to how cardiomyocytes are aggregated together within the ventricular walls. We used pneumatic distension through the coronary arteries to exaggerate the gaps between the aggregated cardiomyocytes, analyzing the pattern revealed using computed tomography, and validating our findings by histology. Methods: We distended 10 porcine hearts, arresting 4 in diastole by infusion of cardioplegic solutions, and 4 in systole by injection of barium chloride. Mural architecture was revealed by computed tomography, measuring also the angulations of the long chains of cardiomyocytes. We prepared the remaining 2 hearts for histology by perfusion with formaldehyde. Results: Increasing pressures of pneumatic distension elongated the ventricular walls, but produced insignificant changes in mural thickness. The distension exaggerated the spaces between the aggregated cardiomyocytes, compartmenting the walls into epicardial, central, and endocardial regions, with a feathered arrangement of transitions between them. Marked variation was noted in the thicknesses of the parts in the different ventricular segments, with no visible anatomical boundaries between them. Measurements of angulations revealed intruding and extruding populations of cardiomyocytes that deviated from a surface-parallel alignment. Scrolling through the stacks of tomographic images revealed marked spiraling of the aggregated cardiomyocytes when traced from base to apex. Conclusion: Our findings call into question the current assumption that cardiomyocytes are uniformly aggregated together in a tangential fashion. There is marked heterogeneity in the architecture of the different ventricular segments, with the aggregated units never extending in a fully transmural fashion.This document was downloaded for personal use only. Unauthorized distribution is strictly prohibited.

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Section: Histological Findingsmentioning

confidence: 84%

Section: Computed Tomographymentioning

confidence: 99%

mentioning

confidence: 99%

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Pneumatic Distension of Ventricular Mural Architecture Validated Histologically

Burg

Lunkenheimer

Niederer

et al. 2016

Fortschr Röntgenstr

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“…In this section we propose a strategy to deal with inexact solutions of the inner subproblems that preserve the convergence property of the iterative procedure. The crucial point of the proposed scheme is devising a suitable stopping criterion for the inner solver of subproblems (6). To explain this novel scheme, we recall the basic definition and some results about the ϵ-subgradient of a proper convex function.…”

Section: The Inexact Iterative Proceduresmentioning

confidence: 99%

Inexact Bregman iteration with an application to Poisson data reconstruction

Benfenati

Ruggiero

2013

Inverse Problems

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Abstract. This work deals with the solution of image restoration problems by an iterative regularization method based on the Bregman iteration. Any iteration of this scheme requires to exactly compute the minimizer of a function. However, in some image reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these subproblems. In this paper, we propose an inexact version of the iterative procedure, where the inexactness in the inner subproblem solution is controlled by a criterion that preserves the convergence of the Bregman iteration and its features in image restoration problems. In particular, the method allows to obtain accurate reconstructions also when only an overestimation of the regularization parameter is known. The introduction of the inexactness in the iterative scheme allows to address image reconstruction problems from data corrupted by Poisson noise, exploiting the recent advances about specialized algorithms for the numerical minimization of the generalized Kullback-Leibler divergence combined with a regularization term. The results of several numerical experiments enable to evaluate the proposed scheme for image deblurring or denoising in presence of Poisson noise.

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“…In recent years, many researchers [8,9,10,12,13,18,22,28,32] study the TV minimization via solving the following saddle-point problem:…”

Section: Introductionmentioning

confidence: 99%

Adaptive Proximal Point Algorithms for Total Variation Image Restoration

Chen

2015

Stat., optim. inf. comput.

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Image restoration is a fundamental problem in various areas of imaging sciences. This paper presents a class of adaptive proximal point algorithms (APPA) with contraction strategy for total variational image restoration. In each iteration, the proposed methods choose an adaptive proximal parameter matrix which is not necessary symmetric. In fact, there is an inner extrapolation in the prediction step, which is followed by a correction step for contraction. And the inner extrapolation is implemented by an adaptive scheme. By using the framework of contraction method, global convergence result and a convergence rate of O(1/N ) could be established for the proposed methods. Numerical results are reported to illustrate the efficiency of the APPA methods for solving total variation image restoration problems. Comparisons with the state-of-the-art algorithms demonstrate that the proposed methods are comparable and promising.

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Primal and Dual Bregman Methods with Application to Optical Nanoscopy

Cited by 71 publications

References 58 publications

Pneumatic Distension of Ventricular Mural Architecture Validated Histologically

Pneumatic Distension of Ventricular Mural Architecture Validated Histologically

Inexact Bregman iteration with an application to Poisson data reconstruction

Adaptive Proximal Point Algorithms for Total Variation Image Restoration

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